The solvability of a boundary-value periodic problem

  • Ya. B. Petrovskii
  • G. P. Khoma

Abstract

In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator.
Published
25.02.1997
How to Cite
PetrovskiiY. B., and KhomaG. P. “The Solvability of a Boundary-Value Periodic Problem”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 2, Feb. 1997, pp. 302–308, https://umj.imath.kiev.ua/index.php/umj/article/view/5006.
Section
Research articles